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代数学コロキウム
過去の記録 ～03/22｜次回の予定｜今後の予定 03/23～
| 開催情報 | 水曜日 17:00～18:00 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 今井 直毅，ケリー シェーン |
2020年05月27日(水)
17:30-18:30 オンライン開催
坂内健一 氏 (慶応大学)
Shintani generating class and the p-adic polylogarithm for totally real fields (ENGLISH)
https://www.ms.u-tokyo.ac.jp/~t-saito/todai_IHES.html
坂内健一 氏 (慶応大学)
Shintani generating class and the p-adic polylogarithm for totally real fields (ENGLISH)
[ 講演概要 ]
In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke $L$-functions for totally real fields. In particular, we will construct a canonical class, which we call the Shintani generating class, in the cohomology of a certain quotient stack of an infinite direct sum of algebraic tori associated with a fixed totally real field. Using our observation that cohomology classes, not functions, play an important role in the higher dimensional case, we proceed to newly define the p-adic polylogarithm function in this case, and investigate its relation to the special value of p-adic Hecke $L$-functions. Some observations concerning the quotient stack will also be discussed. This is a joint work with Kei Hagihara, Kazuki Yamada, and Shuji Yamamoto.
[ 参考URL ]In this talk, we will give a new interpretation of Shintani's work concerning the generating function of nonpositive values of Hecke $L$-functions for totally real fields. In particular, we will construct a canonical class, which we call the Shintani generating class, in the cohomology of a certain quotient stack of an infinite direct sum of algebraic tori associated with a fixed totally real field. Using our observation that cohomology classes, not functions, play an important role in the higher dimensional case, we proceed to newly define the p-adic polylogarithm function in this case, and investigate its relation to the special value of p-adic Hecke $L$-functions. Some observations concerning the quotient stack will also be discussed. This is a joint work with Kei Hagihara, Kazuki Yamada, and Shuji Yamamoto.
https://www.ms.u-tokyo.ac.jp/~t-saito/todai_IHES.html
